Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 5x + 6$ and $ JT = 9x - 10$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {5x + 6} = {9x - 10}$ Solve for $x$ $ -4x = -16$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 5({4}) + 6$ $ JT = 9({4}) - 10$ $ CJ = 20 + 6$ $ JT = 36 - 10$ $ CJ = 26$ $ JT = 26$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {26} + {26}$ $ CT = 52$